On generalized symmetric Finsler spaces

Abstract

In this paper, we study generalized symmetric Finsler spaces. We first study some existence theorems, then we consider their geometric properties and prove that any such space can be written as a coset space of a Lie group with an invariant Finsler metric. Finally we show that each generalized symmetric Finsler space is of finite order and those of even order reduce to symmetric Finsler spaces and hence are Berwaldian.

On Finsler Σ-spaces

“…An isometry on (M, F ) with isolated fixed point x is called a symmetry at x, and is written as s x (see [9]). Proof.…”

“…The study of invariant structure on s−spaces and Σ−spaces is an important problem in differential geometry (see, e.g., [2,3,9]). The purpose of this paper is to study the Finsler Σ−spaces.…”

Generalized Projectively Symmetric Spaces

“…Remark 20. The authors have studied Finsler homogeneous and symmetric spaces [9]; recently Habibi and the second author generalized them to Finsler s-manifolds and weakly Finsler symmetric spaces [10,11]. Therefore these concepts can be mixed and find more generalizations which will be the content of other papers.…”